Problem: Recently Duff has been a soldier in the army. Malek is her commander.

Their country, Andarz Gu has n cities (numbered from 1 to n) and n - 1 bidirectional roads. Each road connects two different cities. There exist a unique path between any two cities.

There are also m people living in Andarz Gu (numbered from 1 to m). Each person has and ID number. ID number of i - th person is i and he/she lives in city number ci. Note that there may be more than one person in a city, also there may be no people living in the city.

<image>

Malek loves to order. That's why he asks Duff to answer to q queries. In each query, he gives her numbers v, u and a.

To answer a query:

Assume there are x people living in the cities lying on the path from city v to city u. Assume these people's IDs are p1, p2, ..., px in increasing order. 

If k = min(x, a), then Duff should tell Malek numbers k, p1, p2, ..., pk in this order. In the other words, Malek wants to know a minimums on that path (or less, if there are less than a people).

Duff is very busy at the moment, so she asked you to help her and answer the queries.

Input

The first line of input contains three integers, n, m and q (1 ≤ n, m, q ≤ 105).

The next n - 1 lines contain the roads. Each line contains two integers v and u, endpoints of a road (1 ≤ v, u ≤ n, v ≠ u).

Next line contains m integers c1, c2, ..., cm separated by spaces (1 ≤ ci ≤ n for each 1 ≤ i ≤ m).

Next q lines contain the queries. Each of them contains three integers, v, u and a (1 ≤ v, u ≤ n and 1 ≤ a ≤ 10).

Output

For each query, print numbers k, p1, p2, ..., pk separated by spaces in one line.

Examples

Input

5 4 5
1 3
1 2
1 4
4 5
2 1 4 3
4 5 6
1 5 2
5 5 10
2 3 3
5 3 1


Output

1 3
2 2 3
0
3 1 2 4
1 2

Note

Graph of Andarz Gu in the sample case is as follows (ID of people in each city are written next to them):

<image>

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
const int MAX_N = 100010;
const int inf = 1000000000;
std::vector<int> g[MAX_N];
int up[MAX_N][20];
int size[MAX_N][20];
int min[MAX_N][20][10];
int h[MAX_N];
std::vector<int> c[MAX_N];
int buf[40];
void Merge(int* min1, int n1, int* min2, int n2, int* min3, int n3) {
  std::merge(min2, min2 + n2, min3, min3 + n3, buf);
  for (int i = 0; i < n1; ++i) {
    min1[i] = buf[i];
  }
}
void dfs(int v, int p, int depth) {
  h[v] = depth;
  up[v][0] = p;
  size[v][0] = std::min(10, (int)c[v].size());
  for (int i = 0; i < size[v][0]; ++i) {
    min[v][0][i] = c[v][i];
  }
  for (int i = 1; i < 20; ++i) {
    up[v][i] = up[up[v][i - 1]][i - 1];
    size[v][i] = std::min(10, size[v][i - 1] + size[up[v][i - 1]][i - 1]);
    Merge(min[v][i], size[v][i], min[v][i - 1], size[v][i - 1],
          min[up[v][i - 1]][i - 1], size[up[v][i - 1]][i - 1]);
  }
  for (int i = 0; i < (int)g[v].size(); ++i) {
    int to = g[v][i];
    if (to != p) {
      dfs(to, v, depth + 1);
    }
  }
}
void Print(int* a, int len) {
  int new_len = 0;
  for (int i = 0; i < len && a[i] != inf; ++i) {
    ++new_len;
  }
  printf("%d", new_len);
  for (int i = 0; i < new_len; ++i) {
    printf(" %d", a[i]);
  }
  printf("\n");
}
int main() {
  int n, m, q;
  scanf("%d %d %d", &n, &m, &q);
  for (int i = 0; i < n - 1; ++i) {
    int v1, v2;
    scanf("%d %d", &v1, &v2);
    --v1;
    --v2;
    g[v1].push_back(v2);
    g[v2].push_back(v1);
  }
  for (int i = 0; i < m; ++i) {
    int x;
    scanf("%d", &x);
    --x;
    c[x].push_back(i + 1);
  }
  for (int i = 0; i < n; ++i) {
    std::sort(c[i].begin(), c[i].end());
  }
  dfs(0, 0, 0);
  for (int t = 0; t < q; ++t) {
    int v, u, a;
    scanf("%d %d %d", &v, &u, &a);
    --v;
    --u;
    if (h[v] < h[u]) {
      std::swap(u, v);
    }
    int ans[10];
    for (int i = 0; i < a; ++i) {
      ans[i] = inf;
    }
    int cur = v;
    if (u != v) {
      for (int i = 19; i >= 0; --i) {
        if (h[cur] - (1 << i) >= h[u]) {
          Merge(ans, a, ans, a, min[cur][i], size[cur][i]);
          cur = up[cur][i];
        }
      }
    }
    int cur_v = cur, cur_u = u;
    if (cur != u) {
      for (int i = 19; i >= 0; --i) {
        if (up[cur_v][i] != up[cur_u][i]) {
          Merge(ans, a, ans, a, min[cur_v][i], size[cur_v][i]);
          Merge(ans, a, ans, a, min[cur_u][i], size[cur_u][i]);
          cur_v = up[cur_v][i];
          cur_u = up[cur_u][i];
        }
      }
      Merge(ans, a, ans, a, min[cur_v][0], size[cur_v][0]);
      Merge(ans, a, ans, a, min[cur_u][0], size[cur_u][0]);
      cur_v = up[cur_v][0];
      cur_u = up[cur_u][0];
    }
    int new_ans[10];
    for (int i = 0; i < std::min(a, (int)c[cur_v].size()); ++i) {
      new_ans[i] = c[cur_v][i];
    }
    Merge(ans, a, ans, a, new_ans, std::min(a, (int)c[cur_v].size()));
    Print(ans, a);
  }
  return 0;
}